You can use TweetSharp v2.3.1. It supports Twitter API 1.1 and it also provides full .NET Framework 3.5 (and also 2.0) support.
You can get it via NuGet or GitHub: if you use NuGet Package Manager, you can just install it from the Command Window by doing that:
Install-Package TweetSharp
I can personally guarantee that it works because I used it in an old 3.5 project and I managed to make it work.
IMPORTANT NOTE: if your project doesn't include Newtonsoft Json.NET >= 5.0.6 (which is a required dependance) NuGet will automatically try to get an updated version which could give you .NET 3.5 compatibility issues. If you run into this issue, just download Json.NET v5.0.6 manually, delete all the stuff downloaded by NuGet (including the .refresh file) and replace them with the Json.NET dll files you downloaded (those in the /Net35/ folder).
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…